Answer
$x=-\frac{3}{2}$ or $x=\frac{1}{3}$
Work Step by Step
We solve by factoring:
$3x^{-2}-7x^{-1}-6=0$
$(3x^{-1}+2)(x^{-1}-3)=0$
$(3x^{-1}+2)=0$ or $(x^{-1}-3)=0$
$3x^{-1}=-2$ or $x^{-1}=3$
$x^{-1}=-\frac{2}{3}$ or $x^{-1}=3$
$x=(-\frac{2}{3})^{-1}$ or $x=3^{-1}$
$x=-\frac{3}{2}$ or $x=\frac{1}{3}$